Validation of spectral MSE for Alcator C-Mod and for ITER

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1 Validation of spectral MSE for Alcator C-Mod and for ITER K.T. Liao 1, W.L. Rowan 1, R.T. Mumgaard 2, Bob Granetz 2, Steve Scott 3, Fred Levinton 4, Howard Yuh 4, O. Marchuk 5, Y. Ralchenko 6 1 The University of Texas at Austin, Institute for Fusion Studies, 2 MIT, Plasma Sciences and Fusion Center, 3 Princeton Plasma Physics Lab, 4 Nova Photonics, Princeton, NJ 5 Forschungszentrum Jülich, 6 National Institute for Standards and Technology 2015 US/EU Transport Task Force Workshop - Salem, MA April 28-May 1, 2014 Salem, MA

2 Introduction Motional Stark Effect (MSE) diagnostics are part of the essential set of diagnostics on most magnetic fusion experiments. MSE provides accurate measurements of magnetic pitch, q, and current profiles. Most MSE diagnostics are based on polarimetry measurements, which offer high signal and fast, reliable measurements. ITER will require a complicated set of optics due to radiation constraints. Polarization aberrations will be high due to heavy coating of the mirrors. There is some interest in using a different kind of MSE diagnostic on ITER, based on spectral measurements (MSE-LS or B- Stark), in order to avoid some of the problems. Alcator C-mod is uniquely capable of demonstrating the effectiveness of spectral methods MSE at ITER-like Stark splitting and density. We have made proof of principle measurements which have been used to test the Line Ratio and Line Shift techniques and validate the MSE spectral model used. We have optimized the hardware for pitch angle sensitivity by increasing spectral resolution and reducing aperture broadening in preparation for an experiment this year which will test the diagnostic at ITER-like conditions.

3 Physics of MSE Spectrum Fast beam atoms moving through a B field experience a Lorentz E field E L Stark Effect: E L field splits energy levels Emission is polarized: π parallel projection of E L σ perpendicular proj. of E L In nkm parabolic basis: (atomic units) [14]

4 Different Types of MSE Diagnostics Line Polarization (MSE-LP) measures pitch angle Line Ratio (MSE-LR) measures pitch angle B-Stark Line Shift (MSE-LS) measures B

5 Pros/Cons Line Polarization MSE Groups multiple lines for high signal Insensitive to broadening allows high signal Need to alter bandpass filters for different beam energy and B field Polarization aberrations drift over time Less obvious if signal is correctly modeled Line Shift MSE Robust calibration, not sensitive to transmission variations in optics Hard to resolve distinct lines Requires a very good model of spectrum and background Line Ratio MSE Strongly affected by non-statistical beam excited population Sensitive to polarization transmission drift Somewhat sensitive to transmission variations in optics Hard to resolve distinct lines Requires a very good model of spectrum and background

6 ITER Advantages for Spectral MSE Excellent line separation from high E L High energy beams (high Doppler shift) No fractional energy components in beam due to negative ion extraction High magnetic field (5.3 T) Measure both B and pitch angle Disadvantages of MSE-LP Difficult to control polarization aberration drift within shot Coating of mirrors and other optics Thermal swings Performance projection from Foley et al (2008) [1,2]: MSE-LS: MSE-LP:

7 MSE spectrum is currently being measured We measured the MSE spectrum for a plasma Blocking bar on D α model Since then, we have improved measurements by decreasing slit width, and decreasing MSE optical aperture width parallel to the beam velocity Spectral resolution is expected to improve by a factor of two

8 Spectral Fitting Fitting of lines requires carefully constrained fit due to overlapping components Line width constrained using previous beam-into-gas measurement model validation is based on full energy component only We constrain model to just 6 independent parameters P 3,0,0 (E=E 0 ) + P 3,0, ±2 (E=E 0 ) P 3,±1, ±1 (E=E 0 ) P 3,±-2,0 (E=E 0 ) ΣP 3,all (E=E 0 /2) ΣP 3,all (E=E 0 /3) R σπ (optical transmission ratio between σ and π polarized emission) While fitting line ratios, the line shifts are determined by magnetic pitch from Kinetic EFIT model.

9 Validation: 1/ 0, 4 / 3 and / CR model gives good match at high n e Some discrepancy at low n e remains Statistical model clearly inadequate Bespamyatnov (2013) [11]

10 ITER extrapolation of MSE line ratios The nkm-resolved CR model predicts a much larger deviation from statistical population for ITER high energy beams than for C-Mod However, the nkm-resolved model still under-predicts the deviation at low n e We assume that the nkm-resolved model will under-predict the deviation for the ITER case by the same value. In this way, we extrapolate the expected deviation from a statistical model to ITER beams Bespamyatnov (2013) [11]

11 Spectral Measurements of MSE Line Ratio

12 , degrees Pitch angle measurement (MSE-LR) Alternatively, using the nkm-resolved CR model, it is possible to measure pitch angle from line ratios (MSE-LR) 12 spectra from 5 viewing chords from shot were used Ohmic mode: t = sec. Kinetic EFIT constrains (q 0 = 0.9, sawtooth inversion radius = m, TS pressure profiles, V loop = 0.96)

13 q profile (MSE-LR) q-profile is reconstructed from pitch angle measurements using simplified equation from Giannella [12]

14 Spectral Measurements of MSE Line Shift

15 Line Shift Measurement Analysis of line shifts requires an accurate model of energy levels Quadratic corrections in Stark Effect are important on C-Mod and ITER (up to 1.5% on C-Mod, 1.5-5% on ITER) Zeeman effect is also included as additional 1.5% correction for C-Mod, but may be neglected for ITER ( % effect) Stark+Zeeman eigenvalues are from Isler (1976) [13] Quadratic corrections added as a perturbation

16 B measurement (MSE-LS) 12 spectra from 5 viewing chords from shot were used Ohmic mode: t = sec. Constrain using kinetic EFIT

17 q profile (MSE-LS) Obtain q using Giannella equation and

18 Improved Measurements Coming Soon We are in progress of taking improved measurements of spectral MSE, using the polarimetry MSE optics Progress: Installed smaller spectrometer slits: 90um 40um (instrument function width 1.8A 1.15A) Reduced MSE aperture to 50% closed Tested using beam into gas without fields: spectral resolution was doubled Planning experiment to test diagnostic (scheduled for 2015) Run with higher field to increase line separation: B T = 8T Optimize beam to increase current and reduce beam divergence to get higher density in plasma This material is based upon work supported by the U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences under Award Number DE-FG03-96ER54373.

19 MSE Spectral Model Spectral Model includes Stark+Zeeman effect quadratic Stark effect beam source area broadening beam divergence broadening parameter variation across beam width aperture/focal broadening beam energy ripple broadening instrumental broadening photon shot noise fractional energy beam components bremsstrahlung background CXRS of thermal D and fast H todo: molecular H 2 background

20 Beam and Aperture Broadening Spread of Doppler angles due to finite size of aperture and beam This translates to a broadening of the BES spectrum BES view, full energy component We calculate the angular spread by casting rays from a lattice of starting and ending points and stepping through the beam intersection Aperture broadening is a major contributor to our line width, so reducing aperture size was necessary

21 Comparison of Broadening Sizes Variation of MSE angles due to finite size of elements (radian) Effect base case beam grid 16cm aperture 5cm spot focus 1.6cm beam width 10cm Doppler shift π:σ ratio polarization Stark split v, s, and B are the directions of the beam, view, and magnetic field, respectively, and v and s are the projection of the beam and view on the plane perpendicular to B. Aperture broadening (by variation of Doppler shift) is the dominant broadening Smaller broadening due to variation of Stark splitting across beam width Reducing the aperture also reduces the signal level, so we may not want to reduce aperture below 1.6cm, when other broadening effects become dominant

22 Improving Line Resolution E L = 13.8 MV/m E L = 23.1 MV/m Resolving lines at 4.45 T is difficult with 50keV beam Better resolution at smaller aperture and higher Lorentz E field C-Mod DNB C-Mod DNB ITER DNB ITER HNB E beam 50 kev 50 kev 100 kev 500 kev? B 5.3 T 8 T 5.3 T 5.3 T 16.4 MV/m 24.8 MV/m 23.2 MV/m 51.9 MV/m

23 Synthetic Diagnostic open aperture 4.5 T 110 um slit half aperture 7.5 T 40 um slit Previous parameters New parameters Smaller slit size and aperture reduce the signal, but improve the spectral resolution, and also reduce the background The new parameters improve the visibility of individual lines We are still working on fitting the synthetic data

24 References 1. E.L. Foley et al. Nucl. Fusion 48 (2008) E.L. Foley et al. Rev. Sci. Instr F521 (2008) 3. F.M. Levington, et al. Phys. Rev. Lett (1989) 4. W. Mandl et al. Plasma Phys. Control. Fusion (1993) 5. K. Jakubowska et al. Rev. Sci. Instr (2004) 6. N.A. Pablant et al. Rev. Sci. Instr F517 (2008) 7. Yu.V. Ralchenko et al. Quant. Spectr. Radiat. Transfer (2001) 8. O. Marchuk et al. J. Phys. B: At. Mol. Opt. Phys (2010) 9. O. Marchuk et al. Plasma Phys. Control. Fusion (2012) 10.Yu.V. Ralchenko et al. Rev. Sci. Instr D504 (2012) 11.I.O. Bespamyatnov et al. Nucl. Fusion, (2013) 12.R. Giannella et al. Rev. Sci. Instrum., 75, 10, (2004) 13.R.C. Isler, Phys. Rev. A, 14 3 (1976) 14.H.A. Bethe and E.E. Salpeter. Quantum Mechanics of One- and Two- Electron Atoms (Berlin: Springer) (1957)

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